Passive entry systems for vehicles are provided on some vehicles to permit a vehicle user who is in possession of the vehicle key to simply pull the door handle and open the door without the need to introduce the key into a keyhole in the door. The key (more particularly, the key fob) is equipped with an electronic device that communicates with the vehicle's on-board control system to authenticate the user. When the user pulls the door handle to indicate that he/she wishes entry into the vehicle, it would be advantageous for the vehicle to unlock the door relatively quickly so that he/she does not have to wait an unduly long time before being permitted to open the door.